BEIJING/FRANKFURT (Reuters) - Tesla has cut prices in a number of its major markets - including in China and Germany - after price cuts in the United States - as it grapples with falling sales and an intensifying price war for electric vehicles (EVs), especially against cheaper Chinese EVs.

The swathe of price cuts comes after Elon Musk's EV maker reported this month that its global vehicle deliveries in the first quarter fell for the first time in nearly four years.

Tesla cut the starting price of the revamped Model 3 in China by 14,000 yuan ($1,930) to 231,900 yuan ($32,000), its official website showed on Sunday.

In Germany, the carmaker trimmed the price of its Model 3 rear wheel drive to 40,990 euros ($43,670.75) from 42,990 euros, where the price has been since February.

There were also price cuts in many other countries in Europe, the Middle East and Africa, a Tesla spokesperson said.

The carmaker cut US prices of its Model Y, Model X and Model S vehicles by $2,000 on Friday. On Saturday it slashed the price of its Full Self-Driving driver assistant software to $8,000 from $12,000 in the United States.

The EV maker has been slow to refresh its ageing models as high interest rates have sapped consumer appetite for big-ticket items, while rivals in China, the world's largest auto market, are rolling out cheaper models.

This weekend, Musk postponed a planned trip to India, where he was to have met Prime Minister Narendra Modi, citing obligations at Tesla. The trip was to have included the announcement of plans for Tesla to enter the South Asian market, Reuters reported on Saturday.

Musk said last Monday that Tesla will lay off more than 10% of its global workforce as the automaker braces for its first annual drop in deliveries.

The announcement came after Reuters reported on April 5 that Tesla had scrapped its plan to develop its long-awaited affordable EV in favour of robotaxis. Musk posted that "Reuters is lying" after the report, without citing any inaccuracies. He has not spoken further about the model, leaving investors clamouring for clarity.

Tesla shares have fallen 40.8% so far this year.